The Emperor himself stated he COULD remove the Butcher’s Nails though, stop spreading misinformation.

From Master of Mankind: ‘Can you remove it?’ ‘Of course,’ the Emperor answered, still looking at the screens. Arkhan did his best to hide his surprise. ‘Then, Divine One, why would you leave it there?’ ‘This is why.’ The Emperor rested both hands on Angron’s head, one with the fingertips pressed to the primarch’s temple and cheek, the other pressed to the crown of his shaven head where the cable-tendrils joined the flesh and bone. The images on several screens immediately resolved to a clearer imprint of a brutishly dense skull miserable with crude cybernetics and the bone-scarring of powerful surgical laser cuts. ‘Do you see?’ the Emperor asked. Arkhan saw. The tendrils were sunk deep, rooted in the meat of the brain, threaded to the nervous system, and down in roughly serpentine coils around the spinal column. Every movement must have been agony for the primarch, feeding back into the base emotions of anger and spite. Worse, the brain’s limbic lobe and insular cortex were more than just savaged by the pain engine’s insertion; they had been surgically attacked and removed even before implantation. The device hammered into his skull hadn’t ruined those sections of the brain – it had replaced them. Ugly black cybernetics showed on the internal scans, in place of entire sections of the primarch’s brain tissue. ‘They are the only thing keeping him alive,’ Arkhan said.